Local finiteness for real-virtual corrections to electroweak production in partonic collisions

TL;DR

This paper introduces a local subtraction scheme for NNLO QCD corrections that allows for numerical integration of loop and phase space in electroweak production processes, improving precision in collider physics.

Contribution

The authors develop a novel local subtraction method based on process-independent subtraction terms and integrand modifications, enabling fully numerical NNLO calculations for hadron collider processes.

Findings

All infrared singularities are subtracted at the integrand level.

The scheme is based on process-independent subtraction terms from single-Higgs production.

It enables local, gauge-invariant, four-dimensional numerical integration.

Abstract

We present a local subtraction scheme that enables the combined integration of loop momenta and the final-state parton phase space in real-virtual NNLO QCD corrections to cross sections for hadroproduction of electroweak and other colorless states. All initial- and final-state infrared singularities are subtracted at the integrand level in momentum space, yielding a locally finite integral ready for numerical integration in four dimensions. The subtraction terms are all based on the well-understood process of single-Higgs production. The core of our subtraction scheme relies on achieving local factorization in all infrared limits of real and virtual momenta. This necessitates systematic modifications of the original Feynman integrand for loop amplitudes, enabling gauge symmetry cancellations before performing integrations. Our approach provides an essential step toward NNLO cross-section calculations for hadron collider processes, where both loop and phase-space integrations are carried out numerically.